Explain mathematically the following statement: Cost minimization does not necessarily imply profit maximization, using the following...

 

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Explain mathematically the following statement: "Cost minimization does not necessarily imply profit maximization," using the following information. ◆ Constrained-cost minimization problem The objective function is Total Cost → TC = w x L + rx K and the constraint is | f(L,K) = Q* where: ← Prescribed output level ◆ Profit maximization problem Maximize{II = II (L,K)} Total Profit → II = II (L, K) = TR - TC Total Revenue → TR = P x Q, Q=f(L,K) ← Production function Total Cost →→ TC = w x L + rx K Explain mathematically the following statement: "Cost minimization does not necessarily imply profit maximization," using the following information. ◆ Constrained-cost minimization problem The objective function is Total Cost → TC = w x L + rx K and the constraint is | f(L,K) = Q* where: ← Prescribed output level ◆ Profit maximization problem Maximize{II = II (L,K)} Total Profit → II = II (L, K) = TR - TC Total Revenue → TR = P x Q, Q=f(L,K) ← Production function Total Cost →→ TC = w x L + rx K